PHYS 142 CH 26 Sarah Eno1 Materials for Lecture Poling cards Demos: J4-01 J4-22 J4-51 Animations courtesy of: T E S T I N G

PHYS 142 CH 26 Sarah Eno2 Capacitors Fields near point charges is all well and good, but let’s do something practical! Capacitors are found in all electric circuits. Capacitor Industries, Inc Chicago, IL

PHYS 142 CH 26 Sarah Eno3 Capacitors A capacitor is a way of storing charge. The symbol for a capacitor in a schematic for an electrical circuit shows basically what it is: two plates with a gap. The charges are held together on the plates by their attraction. (often want to store charge so that it can provide current)

PHYS 142 CH 26 Sarah Eno4 Storing Charge Let’s think about storing charge… Often, you want to store as much charge as possible, while avoiding large (dangerous) voltages For a fixed voltage, you can increase the charged stored by increasing A or decreasing d

PHYS 142 CH 26 Sarah Eno5 Capacitance Or the charge you can store per volt is related to the geometry of the plates and the gap Capacitance is the amount of charge you can store per volt, or Q/V. Farad=coulomb/volt

PHYS 142 CH 26 Sarah Eno6 Increasing Area

PHYS 142 CH 26 Sarah Eno7 Test Yourself I’m going to charge these plates to 1000 V. I’m going to remove the charger, then I’m going to move them apart. As I move them, will the voltage 1)Increase 2)Decrease 3)Stay the same Demo j4-01

PHYS 142 CH 26 Sarah Eno8 Example What would be the area of a capacitor with a gap of ½ mm to have a capacitance of 1 farad?

PHYS 142 CH 26 Sarah Eno9 Example Air breaks down and conducts for an electric field strength of 3x10 6 V/m. How many volts can it hold if it has a gap of 1mm? Capacitors come with voltage ratings. Cheap capacitors can typically hold 50 V.

PHYS 142 CH 26 Sarah Eno10 The Gap What if I stick something inside the gap? Maybe something made of molecules that are electric dipoles… ceramics mica polyvinyl chloride polystyrene glass porcelain rubber electrolyte (glyco-ammonium borate, glycerol-ammonium borate, ammonium lactates, etc dissolved in goo or paste) Dielectric material

PHYS 142 CH 26 Sarah Eno11 Inside: Dipoles Electric Dipole moments in random directions Put a charge on the plates. The charge creates an electric field. Dipole moments try to align with the field.

PHYS 142 CH 26 Sarah Eno12 Capacitors )365 pf, 200V, air variable 2)0.25  F, 3000V, mineral oil 3)21000  F, 25 V, electrolytic 4)20 pF, 100 V, air variable 5)2  F, 400 V, polystyrene 6)100 m F, 12 V, electrolytic 7)10 pf, 200 V, glass/air 8)0.1 m F, 10 V, ceramic 9)0.1 m F, 1 kV, ceramic 10)0.33 m F, 400 V, mylar 11)100 pF, 2kV, ceramic 12)1000 pF, 200V, silver mica 1) Tune radios, 2) filter HV, 3) power supply filter, 4) tune rf, 5) audio 6) audio, 7) vhf/uhf, 8) audio, 9) audio, 10) audio, 11) high power rf, 12) precision rf

PHYS 142 CH 26 Sarah Eno13 Test Yourself Will the field between (and thus the voltage between) the plates be 1)Larger 2)Smaller 3)The same As without the dielectric? Do j4-22

PHYS 142 CH 26 Sarah Eno14 Inside: Fields The field goes down. So, the amount of charge you can put on for 1 volt is larger. So, the capacitance goes up. A certain fraction of the field is “canceled”. E=E 0 /  V=V 0 / . C=  C 0

PHYS 142 CH 26 Sarah Eno15 Dielectrics Material  Breakdown field (10 6 V/m) Air Paper Glass Paraffin Rubber Mica Water 80 0

PHYS 142 CH 26 Sarah Eno16 Example What area would a capacitor with a 0.5 mm gap have to for a capacitance of 1 farad if it had a dielectric constant ( k ) of 10? Found earlier that without dielectric, need an area of 56x10 6 m 2. So, reduce this by 10 to 56x10 5 m 2

PHYS 142 CH 26 Sarah Eno17 Example A typical capacitor has a capacitance of 10  F, a gap of 0.1 mm, and is filled with a dielectric with a dielectric strength of 10. What is the area?

PHYS 142 CH 26 Sarah Eno18 Energy Stored How much work to move some this charge onto the capacitor? Amount of work to charge from scratch. Sum (integral) up the contributions to bring each charge

PHYS 142 CH 26 Sarah Eno19 Energy Stored But, Q is hard to measure

PHYS 142 CH 26 Sarah Eno20 Simple Circuits Let’s try our first simple circuit

PHYS 142 CH 26 Sarah Eno21 Capacitors with a Battery An “ideal” battery is a source of constant voltage. Though it is done using properties of metal, ions, etc, you should think of it as containing a fixed E field. Charge on one side is at a higher potential than the other

PHYS 142 CH 26 Sarah Eno22 Batteries Students have many misconceptions about batteries, which lead to serious difficulties in making predictions about circuits. Batteries are not charged. They do not contain a bunch of electrons, ready to “spit out” Batteries are not current sources. They don’t put out a constant current.

PHYS 142 CH 26 Sarah Eno23 Ground Zero volt point. Reservoir of electrons. Can take and give electrons easily.

PHYS 142 CH 26 Sarah Eno24 Circuits Remember: it takes no work to move an charge through a conductor. The potential does not change! (for an ideal conductor… since only a “superconductor” is an ideal conductor, this is only mostly true for copper, gold, etc)

PHYS 142 CH 26 Sarah Eno25 Test Yourself When I close the switch will the voltage across the battery 1)Go down because charge leaves the battery to go to the capacitor 2)Go up because the battery will get additional charge from the capacitor 3)Stay the same because the voltage across a battery always stays the same

PHYS 142 CH 26 Sarah Eno26 Battery + Capacitor

PHYS 142 CH 26 Sarah Eno27 Example What is the charge on a 1  F capacitor attached to a 1.5 V battery? How many electrons is that?

PHYS 142 CH 26 Sarah Eno28 Capacitor Circuits If you have more than 1 capacitor in a circuit, two basic ways to arrange them parallel series

PHYS 142 CH 26 Sarah Eno29 Parallel Circuits Connected in Parallel How will the voltage across them compare? 1)It will half. The voltage from the battery will be divided between the two 2)It will double. Because there will be two capacitors charged 3)It will be the same. The voltage is always the same.

PHYS 142 CH 26 Sarah Eno30 Parallel Circuits How does the charge compare?

PHYS 142 CH 26 Sarah Eno31 Parallel Twice the charge for the same voltage. Effectively increasing the area of the capacitor

PHYS 142 CH 26 Sarah Eno32 Parallel If you replaced the 2 capacitors with 1 capacitor, what capacitance would it have to have in order to have the same voltage and the same charge -> effective capacitance of the system

PHYS 142 CH 26 Sarah Eno33 Series How will the voltage across them compare? 1)It will half. The voltage from the battery will be divided between the two 2)It will double. Because there will be two capacitors charged 3)It will be the same. The voltage is always the same. The voltage across each is 1/2. That means the charge on each is ½ compared to 1 capacitor circuit.

PHYS 142 CH 26 Sarah Eno34 Series Its like you have twice the gap. The effective capacitance goes down.

PHYS 142 CH 26 Sarah Eno35 Series in General

PHYS 142 CH 26 Sarah Eno36 Check

PHYS 142 CH 26 Sarah Eno37 Hints for Capacitors remember the voltage across a battery is fixed remember voltage does not change along a wire look for parallel and series combinations, and calculate the equivalent capacitance.

PHYS 142 CH 26 Sarah Eno38 Example What is the charge on each cap? What is the voltage across each cap? 1)Look for series and parallel combinations. Calculate equivalent capacitance. Replace. Repeat until have 1 cap. 2)Then work backwards

PHYS 142 CH 26 Sarah Eno39 Example

PHYS 142 CH 26 Sarah Eno40 Example Before the dielectric is added, the capacitance is C 0. What is the capacitance afterwards? Picture it as two caps in series, each with a gap d/2 and therefore capacitance 2C 0. When add dielectric, each capacitance goes up a factor 

PHYS 142 CH 26 Sarah Eno41 Test Yourself Which capacitor has the biggest charge? 1)1  F 2)0.2  F 3)0.6  F 4)They all have the same charge 5)None of the above

PHYS 142 CH 26 Sarah Eno42 Example What is the equivalent capacitance?.6 and.2 are in parallel. Add them to get.8 The 1 and the “.8” are in series.

PHYS 142 CH 26 Sarah Eno43 Fun Another use for capacitance Do j4-51

PHYS 142 CH 26 Sarah Eno44 Hints for Capacitor Problems